Transient analysis of data-normalized adaptive filters

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T. Y. Al-Naffouri and A. H. Sayed, "Transient analysis of data-normalized adaptive filters",  IEEE Transactions on Signal Processing.   vol. 51 , pp. 639-652, Mar 2003.

Abstract:

This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability, of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model provides information about the mean-square deviation and mean-square error performance of the filters. In addition to deriving earlier results in a unified manner, the approach leads to stability and performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and does not require an explicit recursion for the covariance matrix of the weight-error vector.